Aside from aesthetics, planter boxes must be functional in terms of plants' requirements. They must have a means of drainage. Simply cutting several holes about 3/4 inch in diameter in the bottom of each box with a drill-mounted hole saw should provide adequate drainage. (When the boxes are being set up for planting, place coarse gravel or broken shards of old terracotta plant pots as a bottom layer under the potting soil and just above the holes to complete the drainage system.)
Pressure-treated wood will be longer lasting and is fine for flowers and ornamentals. But if herbs or any other edible plants are to be grown in the boxes, pressure-treated wood is definitely not recommended due to toxins that can leech into the soil and be absorbed by the plants' roots. Ordinary untreated pine will hold up fairly well as long as the exterior--especially the cut end grain of the boards--is sealed with a solid latex stain.
The joinery for deck planter boxes needn't be fancy. Ordinary butt joints, in which one piece of wood overlaps the other at the edge (versus angled miter joints), are just fine. Because they'll be exposed continually to the elements--especially water--fasteners should be hot-dipped, galvanized or ceramic-coated deck screws. Stainless steel, although generally more expensive, is another option. Screw length must be adequate for the board thickness. For so-called "1-by" material (boards that are nominally 1-inch thick but actually measure closer to 3/4 inch), 6-by-1 5/8-inch screws are a good choice.
Deck planter boxes can be large or small. Different sizes may be desirable to lend variety to a deck area. Different parts of a deck may accommodate different size planter boxes.
Keep in mind that soil and drainage gravel or other materials are heavy, that water is heavy, and that the plants themselves will contribute increasing weight as they grow. Plus, in a climate where ice and snow accumulate, there could be considerable additional weight on the planter boxes in winter. Sizable lag bolts (hot-dipped galvanized) are probably the best fastener for attaching the planter box to the deck. There should be an adequate number of bolts for the size of the box, and the deck member the bolts are driven into must be up to the task of holding the weight.
Deck planter boxes can be simple or ornate. A few simple curves can break up what would otherwise be a monotonous straight edge. This is obviously a matter of taste and custom design. Be creative.